I think the problem is too much nitrite from too much ammonia. As I noted, in the range of 16 ppm on an API kit it is at a level that harms cycling.
Hobby nitrate kits do not actually test nitrate, they actually convert it to nitrite and measure that. Therefore, when one has nitrite in their water then must also get the reading for this and then subtract it from the nitrate reading.
All sorts of things in the water can affect the test kit results. What depend on which test kit.
The bacteria are much hardier in many respects than most hobbyists realize. They are not so easy to kill. They do not need to be feed every day. This misconception is the most common cause of people deviating from cycling instructions re ammonia and then they end up with too much nitrite.
If you consider that each ppm of ammonia can become 2.55 ppm of nitrite, you can actually do the calculation yourself and know what might be the result. The reason the directions here state the 2nd dose of ammonia not be done unless ammonia is under .75 ppm and nitrite is clearly over 2 ppm is to insure two things, The first is that the tank is processing ammonia but it is also to insure that this is not a testing mistake because it requires one see the nitrite too. The presence of the nitrite is as important as the drop in ammonia.
Also, if one follows the ammonia dosing correctly, it can not produce enough nitrite to become a problem. The regimen was specifically designed so that diluted nitrite testing would not be needed since it makes things much harder for most folks cycling their first tank. The method is pretty much foolproof unless one changes the ammonia dosing.
You have also discovered on of the biggest problems with using hobby test kits, the results are based on color and all of us can see the same result as a different color. Expensive test kits do not rely on the human eye to determine the level, they use a colorimeter to read the exact wavelengths. Anything that can effect the color can cause a bad reading. Some high grade test systems have instructions for how to deal with turbid water or water with iron in it. Theyalso include a list of what can cause testing errors and at what levels they will do so.
Test kits are a big help in giving us an idea of what is up in terms of the direction things are moving and to some extent simply detecting their presence. Where they tend to fall short is at the extremes. For example, very high nitrite can show up as 0 on a hobby kit or ammonia detoxifiers (often in our dechlor) can cause false positives of .25 or .5 ppm on ammonia tests.
This is one reason it can help to know what should be going on. For example if one doses a 3 ppm amount of ammonia and it appears to go down but no nitrite appears, a flag should go up. If a single ppm of that ammonia goes away, it should be making about 2.5 ppm of nitrite. If you test and get 5 ppm, a flag should go up. Too often when the numbers do not add up we ignore that and instead trust the test results anyway.
The best thing you can do here is a huge water change or two to get ammonia and nitrite levels as close to 0 as you can. Then wait at least 24 hours and test to be sure the numbers are down. Then redose the 3 ppm amount, If you have read the cycling article you should see it is recommends one lower the advertised capacity of a tank by 10-15% to allow for the glass and the decor/gravel. Wait another 24 and test for ammonia and nitrite (leave the nitrate kit in the box). The results here should show us where things stand.
What I would expect is the ammonia will have dropped, maybe even close to 0. First, this means you do have ammonia bacs, Second, it will let you calculate how much nitrite you should have by multiplying the ppm drop of ammonia by 2.55. Compare this number to your nitrite test result. Only 3 things can happen here and depending on which, you will know what is up:
1. If the numbers are close to equal, it means you have a fair amount of ammonia bacs but almost no nitrite bacs. You are still early in the cycle.
2. If the number is clearly lower for the actual test than the calculated one, this means you also have some nitrite bacs at work. You are midway through a cycle.
3. If the test result is clearly higher than the calculated number, it means one or more of the following: you have a bad kit, are testing incorrectly or are misreading the color.
Hopefully all of this will get you back on top of your cycle. keep us posted here.